Re: [Phys-l] Relativistic elevator

[John Denker <jsd@av8n.com>]

On 03/25/2008 08:46 AM, Savinainen Antti wrote:

> there are three figures regarding a relativistic elevator & the
> equivalence principle in Strobel's Astronomy Notes:
>
> <http://www.astronomynotes.com/relativity/s3.htm> (Scroll down)
>
> Strobel explains the middle figure thus:
>
> "If your elevator is moving at a constant velocity upward relative to
> the person outside, you will see the beam of light travel in a 
> straight-line path angled downward. The person outside still sees the
> beam travelling in a horizontal direction."
>
> This would mean, of course, that using the abovementioned arrangement
> the observer inside the elevator could deduce that he is moving
> upwards at constant velocity w.r.t. to the source of the light beam.
> Is this consistent with SR? 

Sure.

> If it is then the situation must be
> equivalent to "looking outside".

Yes.  
 1) The shallow answer is that "looking outside" always means "looking
  at light rays that came from outside".  But I think the intent of 
  the question is deeper than that.
 2a) To really understand the physics requires emphasizing the part
  that states the beam is *horizontal* in the lab frame.  That is,
  the slope of the beam in the elevator frame tells you the velocity
  relative to the frame where there was no slope.   For you (the
  elevator rider) to know that the beam was horizontal in the lab 
  frame requires rather detailed "looking outside".
 2b) This is crucial because if you confine your attention to the 
  inside of the elevator, if you see a sloping beam you could perfectly 
  well attribute it to a source who is comoving with the elevator and 
  just holding the flashlight at an angle.  This scenario (2b) would 
  tell you nothing about your velocity relative to the lab frame.
 
> However, the situation in the third figure would not allow the
> elevator observer to resolve whether he/she is in a gravitational
> field or accelerating upwards as implied by the equivalence
> principle. This is also what Strobel states.

That's true.  That's Einstein's equivalence principle, that to first
order in a small region, gravity is indistinguishable from acceleration 
of the reference frame.

Note that careful thinking as in item (2) above is not needed here;  
the beam is curved /within/ the elevator and you don't need to know 
anything about where it came from.  Think about the first three terms 
in the Taylor series, i.e. position, velocity, and acceleration:
 -- translational invariance:  there is no absolute position, just
  relative position
 -- Galilean relativity:  there is no absolute velocity, just
  relative velocity
 ++ There *is* a well-behaved notion of absolute acceleration.

So the third panel of the diagram makes an important contrast with
the second panel.